** Riv.Mat.Univ.Parma (5) 2 (1993)-Parte I **

**LUCILLA BASSOTTI RIZZA**

*Uno schema alle differenze finite per problemi ellittici che conserva le proprietà di simmetria
*

**Pages** 29-44

**Received:** 6 April 1993

**AMS Classification :** 65N06

**Abstract**
Let be Ω a bounded domain of **R**^{n} and L a second order elliptic differential operator. Assume that Ω and L are invariant with respect to a group G of isometries.

A convenient finite difference scheme for the Direchlet problem concerning L and Ω is considered. Existence and some symmetry properties of a solution u of the approximate problem are obtained.
A function u', interpolating u and having the same symmetry properties of exact solution u*, is proposed. Finally, it is shown that u' converges to u* as the diameter of the grid tends to zero.